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Research has shown that people can learn many nouns (i.e., word-referent mappings) from a short series of ambiguous situations containing multiple word-referent pairs. Associative models assume that people accomplish such cross-situational learning by approximately tracking which words and referents co-occur. However, some researchers posit that learners hypothesize only a single referent for each word, and retain and test this hypothesis unless it is disconfirmed. To compare these two views, we fit two models to individual learning trajectories in a cross-situational word-learning task, in which each trial presents four objects and four spoken words-16 possible word-object pairings per trial. The model that maintains a single hypothesis for each word does not fit as well as the associative model that roughly learns the co-occurrence structure of the data using competing attentional biases for familiar pairings …